Answer-first summary for fast verification
Answer: 4,050
**Step-by-step explanation:** 1. **Sort the data in ascending order:** - 2,600 (Week 5) - 2,700 (Week 3) - 2,800 (Week 2) - 3,800 (Week 1) - 4,300 (Week 6) - 9,900 (Week 4) 2. **Calculate the position for the 75th percentile:** - Formula: α × n = 0.75 × 6 = 4.5 - Where α = 0.75 (75th percentile) and n = 6 (number of observations) 3. **Determine the value at position 4.5:** - Since 4.5 is not an integer, we need to take the average of the values at positions 4 and 5 - Position 4: 3,800 (Week 1) - Position 5: 4,300 (Week 6) - Average = (3,800 + 4,300) ÷ 2 = 8,100 ÷ 2 = 4,050 **Key concept:** For quantile/percentile calculation when the position is not an integer, we interpolate between the two nearest data points. The 75th percentile represents the value below which 75% of the observations fall.
Author: Nikitesh Somanthe
Ultimate access to all questions.
The following data represents a sample of daily profit of a sales company for six weeks in a particular year.
| Week | Amount of the Profit($) |
|---|---|
| 1 | 3,800 |
| 2 | 2,800 |
| 3 | 2,700 |
| 4 | 9,900 |
| 5 | 2,600 |
| 6 | 4,300 |
What is the 75% quantile profit?
A
4,000
B
4,234
C
4,050
D
4,654
No comments yet.